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Dermatological diseases are among the most common disorders worldwide. This paper presents the first study of the interpretability and imbalanced semi-supervised learning of the multiclass intelligent skin diagnosis framework (ISDL) using 58,457 skin images with 10,857 unlabeled samples. Pseudo-labelled samples from minority classes have a higher probability at each iteration of class-rebalancing self-training, thereby promoting the utilization of unlabeled samples to solve the class imbalance problem. Our ISDL achieved a promising performance with an accuracy of 0.979, sensitivity of 0.975, specificity of 0.973, macro-F1 score of 0.974 and area under the receiver operating characteristic curve (AUC) of 0.999 for multi-label skin disease classification. The Shapley Additive explanation (SHAP) method is combined with our ISDL to explain how the deep learning model makes predictions. This finding is consistent with the clinical diagnosis. We also proposed a sampling distribution optimisation strategy to select pseudo-labelled samples in a more effective manner using ISDLplus. Furthermore, it has the potential to relieve the pressure placed on professional doctors, as well as help with practical issues associated with a shortage of such doctors in rural areas.